A radioactive decay rate of a radioactive element is found to be 1000 disintegrations per second at a certain time. If the half-life of the element is 1 second, the decay rate after one second is _ and after three seconds is _.

Explanation

The decay of a radioactive substance follows an exponential decay law. The rate of decay at any given time is proportional to the amount of the substance present. The half-life is the time it takes for half of the radioactive substance to decay.Initial decay rate: 1000 disintegrations per second (at t = 0 seconds)After 1 second:Since the half-life is 1 second, after 1 second, half of the radioactive material will have decayed. So, the remaining decay rate will be 500 disintegrations per second (half of the initial rate).After 3 seconds:At this point, the original radioactive substance has decayed to a quarter of its initial amount (2 half-lives). Therefore, the remaining decay rate will be 125 disintegrations per second.Comparing the decay rates:After 1 second: 500 disintegrations per secondAfter 3 seconds: 125 disintegrations per secondThe answer that matches this pattern is A: 500, 125.